A221904 a(n) = 9^n + 10^n.

2, 19, 181, 1729, 16561, 159049, 1531441, 14782969, 143046721, 1387420489, 13486784401, 131381059609, 1282429536481, 12541865828329, 122876792454961, 1205891132094649, 11853020188851841

Offset: 0

Author

Vincenzo Librandi, Feb 06 2013

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (19,-90).

Crossrefs

Cf. A007689, A074611, A074615, A074619, A074622, A074624, A155872.

Programs

Magma

[9^n + 10^n: n in [0..30]];

Mathematica

CoefficientList[Series[1/(1-9*x) + 1/(1-10*x), {x, 0, 30}], x]
LinearRecurrence[{19,-90},{2,19},30] (* Harvey P. Dale, Nov 10 2017 *)

Formula

G.f.: 1/(1 - 9*x) + 1/(1 - 10*x).

E.g.f.: exp(9*x) + exp(10*x).

a(n) = 19*a(n-1) - 90*a(n-2), a(1)=2, a(2)=19.